Information on Result #806405
Linear OOA(270, 74, F2, 2, 20) (dual of [(74, 2), 78, 21]-NRT-code), using OOA 2-folding based on linear OA(270, 148, F2, 20) (dual of [148, 78, 21]-code), using
- construction XX applied to C1 = C({0,1,3,5,7,9,11,13,63}), C2 = C([1,15]), C3 = C1 + C2 = C([1,13]), and C∩ = C1 ∩ C2 = C({0,1,3,5,7,9,11,13,15,63}) [i] based on
- linear OA(257, 127, F2, 17) (dual of [127, 70, 18]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,63}, and minimum distance d ≥ |{−2,−1,…,14}|+1 = 18 (BCH-bound) [i]
- linear OA(256, 127, F2, 18) (dual of [127, 71, 19]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,15], and designed minimum distance d ≥ |I|+1 = 19 [i]
- linear OA(264, 127, F2, 21) (dual of [127, 63, 22]-code), using the primitive cyclic code C(A) with length 127 = 27−1, defining set A = {0,1,3,5,7,9,11,13,15,63}, and minimum distance d ≥ |{−2,−1,…,18}|+1 = 22 (BCH-bound) [i]
- linear OA(249, 127, F2, 14) (dual of [127, 78, 15]-code), using the primitive narrow-sense BCH-code C(I) with length 127 = 27−1, defining interval I = [1,13], and designed minimum distance d ≥ |I|+1 = 15 [i]
- linear OA(21, 9, F2, 1) (dual of [9, 8, 2]-code), using
- discarding factors / shortening the dual code based on linear OA(21, s, F2, 1) (dual of [s, s−1, 2]-code) for arbitrarily large s, using
- linear OA(25, 12, F2, 3) (dual of [12, 7, 4]-code or 12-cap in PG(4,2)), using
- discarding factors / shortening the dual code based on linear OA(25, 16, F2, 3) (dual of [16, 11, 4]-code or 16-cap in PG(4,2)), using
Mode: Constructive and linear.
Optimality
Show details for fixed k and m, n and k, k and s, k and t, n and m, m and s, m and t, n and s, n and t.
Other Results with Identical Parameters
None.
Depending Results
None.